Neither --- it is a branch point. When one integrates a simple pole,
one genrates a logarithm. you can think of it this way. Write
1/ln{z} as 1/(z-1) + f(z) where f is analytic at z = 1 (in other
words, separate out the pole). Integrating, we find that li{z} =
log (z-1) + F(z), where F is the antiderivative of f, which makes it
analytic at z = 1.